Hi,
You wrote: Once the M5Stack is powered off, only the CAN information can no longer be read. So the solution is easy: Power ON the M5 device!
Or do you mean OTHER devices on the same CAN are not able to read data WHILE M5 is OFF? In this case it might be possible that the CAN transceiver in the Commu is still powered (check that!) but miss the input signal. According to the datasheet of the CAN driver chip the bus output is dominant while TXD and S pins are LOW. This blocks the communication of other devices. It may help to solder the pin 8 of the transceiver to +3.3V instead of GND to enable silent mode (switch it to Rx only) or make sure the commu is not powered. The bus driver is then going to float (Off Mode) and should not block the communication anymore.